Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x+8y &= -5 \\ -4x-4y &= 5\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-4x = 4y+5$ Divide both sides by $-4$ to isolate $x$ $x = {-y - \dfrac{5}{4}}$ Substitute this expression for $x$ in the first equation. $-2({-y - \dfrac{5}{4}}) + 8y = -5$ $2y + \dfrac{5}{2} + 8y = -5$ Simplify by combining terms, then solve for $y$ $10y + \dfrac{5}{2} = -5$ $10y = -\dfrac{15}{2}$ $y = -\dfrac{3}{4}$ Substitute $-\dfrac{3}{4}$ for $y$ in the top equation. $-2x+8( -\dfrac{3}{4}) = -5$ $-2x-6 = -5$ $-2x = 1$ $x = -\dfrac{1}{2}$ The solution is $\enspace x = -\dfrac{1}{2}, \enspace y = -\dfrac{3}{4}$.